Which of the following is rational?(1 point) Responses 3–√ +3–√ 3–√ +3–√ 13√ the fraction with numerator 1 and denominator square root of 3 3 −−√ × 3–√ 3 −−√ × 3–√ 3√1

Answer 1

To determine which of the given expressions is rational, let's analyze each one step-by-step.

1. \( \sqrt{3} + \sqrt{3} \): This simplifies to \( 2\sqrt{3} \), which is irrational since \( \sqrt{3} \) is irrational.

2. \( \frac{1}{\sqrt{3}} \): This is also irrational, but if we rationalize the denominator, we multiply by \( \frac{\sqrt{3}}{\sqrt{3}} \), which gives us \( \frac{\sqrt{3}}{3} \). This expression is still irrational.

3. \( \sqrt{3} \times \sqrt{3} \): This gives us \( 3 \), which is a rational number.

4. \( \sqrt{3} \cdot 1 \): This is simply \( \sqrt{3} \), which is irrational.

Based on the analysis, the only rational expression is \( \sqrt{3} \times \sqrt{3} = 3 \). So the correct answer is:

3 (the product of \( \sqrt{3} \) with itself).